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PRINTABLE VERSIONQuiz 10

Question 1

The z-score associated with the 96.5 percent confidence interval is

a) 2.108

b) 1.812

c) 1.767

d) 2.012

e) 2.611

f) None of the above

Question 2

What will reduce the width of a confidence interval?

a) Increase variance.

b) Increase confidence level.

c) Decrease variance.

d) Decrease number in sample.

Question 3

A simple random sample of 49 8th graders at a large suburban middle school indicated that 88% of them areinvolved with some type of after school activity. Find the margin of error associated with a 90% confidenceinterval that estimates the proportion of them that are involved in an after school activity.

a) 0.046

b) 0.076

c) 0.060

d) 0.260

e) 0.126

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f) None of the above

Question 4

A simple random sample of 100 8th graders at a large suburban middle school indicated that 82% of themare involved with some type of after school activity. Find the 95% confidence interval that estimates theproportion of them that are involved in an after school activity.

a) [0.745, 0.895]

b) [0.745, 0.695]

c) [0.795, 0.800]

d) [0.645, 0.845]

e) [0.665, 0.895]

f) None of the above

Question 5

Mars Inc. claims that they produce M&Ms with the following distributions:

Brown 30% Red 20% Yellow 20% Orange 10% Green 10% Blue 10%

A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were:

Brown 23 Red 21 Yellow 22 Orange 14 Green 17 Blue 14

Find the 97% confidence interval for the proportion of yellow M&Ms in that bag.

a) [0.116, 0.280]

b) [0.016, 0.230]

c) [0.166, 0.171]

d) [0.116, 0.080]

e) [0.036, 0.280]

f) None of the above

Question 6

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Mars Inc. claims that they produce M&Ms with the following distributions:

Brown 30% Red 20% Yellow 20% Orange 10% Green 10% Blue 10%

A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were:

Brown 24 Red 24 Yellow 19 Orange 14 Green 16 Blue 15

Find the 99% confidence interval for the proportion of blue M&Ms in that bag.

a) [0.101, 0.106]

b) [0.051, 0.017]

c) [0.051, 0.217]

d) [-0.029, 0.217]

e) [-0.049, 0.167]

f) None of the above

Question 7

Mars Inc. claims that they produce M&Ms with the following distributions:

Brown 30% Red 20% Yellow 20% Orange 10% Green 10% Blue 10%

How many M&Ms must be sampled to construct the 98% confidence interval for the proportion of brownM&Ms in that bag if we want a margin of error of ± .15?

a) 51

b) 40

c) 53

d) 39

e) 50

f) None of the above

Question 8

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An experimenter flips a coin 100 times and gets 56 heads. Find the 96.5% confidence interval for theprobability of flipping a head with this coin.

a) [0.355, 0.615]

b) [0.375, 0.665]

c) [0.455, 0.665]

d) [0.505, 0.510]

e) [0.455, 0.465]

f) None of the above

Question 9

Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How manytimes would we have to flip the coin in order to obtain a 85% confidence interval of width of at most .11 forthe probability of flipping a head?

a) 89

b) 88

c) 172

d) 177

e) 171

f) None of the above

Question 10

It has been observed that some persons who suffer renal failure are diagnosed with it again within one yearof the first episode. This is due, in part, to damage from the first episode. In order to examine the percentageof the persons who suffer renal failure a second time, a random sample of 1100 people who suffered renalfailure was collected. It was observed that 17 of them again suffered renal failure within one year. Select a90% confidence interval for the true proportion of those who suffer a second episode.

a) [0.0114, 0.0516]

b) [0.0144, 0.0716]

c) [0.0124, 0.0416]

d) [0.00936, 0.0216]

e) [0.0104, 0.0616]

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f) None of the above

Question 11

When solving for the sample size required to estimate p to within a particular margin of error, under whatcircumstances do we use p̂ = .5?

a) When the variance is equal to .5 or when we desire a most conservative sample size.

b) When the computed value of p̂ = .5

c) When p̂ = .4 and 1 - p̂ = .6

d) When we have no prior information on the approximate value of p̂ or p.

e) When the margin of error desired is less than or equal to .5

f) None of the above

Question 12

Television viewers often express doubts about the validity of certain commercials. In an attempt to answertheir critics, a large advertiser wants to estimate the true proportion of consumers who believe what is shownin commercials. Preliminary studies indicate that about 40% of those surveyed believe what is shown incommercials. What is the minimum number of consumers that should be sampled by the advertiser to be95% confident that their estimate will fall within 3% of the true population proportion?

a) 1036

b) 1017

c) 1010

d) 1031

e) 1025

f) None of the above

Question 13

An oil company is interested in estimating the true proportion of female truck drivers based in five southernstates. A statistician hired by the oil company must determine the sample size needed in order to make theestimate accurate to within 2% of the true proportion with 90% confidence. What is the minimum number oftruck drivers that the statistician should sample in these southern states in order to achieve the desiredaccuracy?

a) 1710

b) 1699

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c) 1685

d) 1680

e) 1692

f) None of the above

Question 14

It has been observed that some persons who suffer colitis, again suffer colitis within one year of the firstepisode. This is due, in part, to damage from the first episode. The performance of a new drug designed toprevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to dothis two groups of people suffering a first episode are selected. There are 112 people in the first group andthis group will be administered the new drug. There are 147 people in the second group and this group wil beadministered a placebo. After one year, 13% of the first group has a second episode and 20% of the secondgroup has a second episode. Select a 99% confidence interval for the difference in true proportion of the twogroups.

a) [-0.048, 0.065]

b) [-0.072, 0.212]

c) [-0.188, 0.048]

d) [-0.688, 0.548]

e) [-0.212, 0.072]

f) None of the above

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PRINTABLE VERSIONQuiz 11

Question 1

As the length of the confidence interval for the population mean decreases, the degree of confidence in theinterval's actually containing the population mean

a) decreases

b) does not change

c) increases

Question 2

The gas mileage for a certain model of car is known to have a standard deviation of 6 mi/gallon. A simplerandom sample of 64 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gallon.Construct a 97.5% confidence interval for the mean gas mileage for this car model.

a) [15.740, 39.260]

b) [25.819, 29.181]

c) [27.290, 27.710]

d) [26.030, 28.970]

e) [14.054, 40.946]

f) None of the above

Question 3

If the 90% confidence limits for the population mean are 57 and 63, which of the following could be the 98%confidence limits

a) [56, 61]

b) [56, 64]

c) [60, 60]

d) [59, 63]

e) [58, 65]

f) None of the above

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Question 4

A 95% confidence interval for the mean of a population is to be constructed and must be accurate to within0.3 unit. A preliminary sample standard deviation is 1.5. The smallest sample size n that provides the desiredaccuracy is

a) 97

b) 91

c) 109

d) 101

e) 93

f) None of the above

Question 5

An SRS of 24 students at UH gave an average height of 6.1 feet and a standard deviation of .3 feet.Construct a 90% confidence interval for the mean height of students at UH.

a) [4.600, 7.900]

b) [6.079, 6.121]

c) [5.995, 6.205]

d) [5.586, 6.614]

e) [4.850, 7.550]

f) None of the above

Question 6

Which test statistic should be used when computing a confidence interval given only the number in a sample,the population standard deviation and sample mean?

a) μ

b) t

c) z

Question 7

Location is known to affect the number, of a particular item, sold by Walmart. Two different locations, A andB, are selected on an experimental basis. Location A was observed for 18 days and location B was observed

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for 18 days. The number of the particular items sold per day was recorded for each location. On average,location A sold 39 of these items with a sample standard deviation of 9 and location B sold 55 of these itemswith a sample standard deviation of 6. Select a 99% confidence interval for the difference in the true meansof items sold at location A and B.

a) [48.42, 61.58]

b) [32.42, 45.58]

c) [-22.95, -9.05]

d) [87.42, 100.6]

e) [-18.55, -13.45]

f) None of the above

Question 8

An auditor for a hardware store chain wished to compare the efficiency of two different auditing techniques.To do this he selected a sample of nine store accounts and applied auditing techniques A and B to each of thenine accounts selected. The number of errors found in each of techniques A and B is listed in the tablebelow:

Errors in A Errors in B45 3148 3746 3948 3752 5450 4549 4940 4145 50

Select a 90% confidence interval for the true mean difference in the two techniques.

a) [3.050, 5.838]

b) [-4.183, 4.183]

c) [2.584, 6.304]

d) [2.195, 6.693]

e) [0.261, 8.627]

f) None of the above

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Question 9

A toy maker claims his best product has an average lifespan of exactly 14 years. A skeptical quality controlspecialist asks for evidence (data) that might be used to evaluate this claim. The quality control specialistwas provided data collected from a random sample of 45 people who used the product. Using the data, anaverage product lifespan of 19 years and a standard deviation of 4 years was calculated. Select the 99%,confidence interval for the true mean lifespan of this product.

a) [-1.5384, 1.5384]

b) [12.462, 15.538]

c) [17.211, 20.789]

d) [17.462, 20.538]

e) [18.771, 19.229]

f) None of the above

Question 10

An important problem in industry is shipment damage. A pottery producing company ships its product bytruck and determines that it cannot meet its profit expectations if, on average, the number of damaged itemsper truckload is greater than 11. A random sample of 15 departing truckloads is selected at the delivery pointand the average number of damaged items per truckload is calculated to be 11.3 with a calculated sample ofvariance of 0.64. Select a 90% confidence interval for the true mean of damaged items.

a) [10.68, 11.92]

b) [10.64, 11.36]

c) [53.67, -33.86]

d) [-0.3635, 0.3635]

e) [10.94, 11.66]

f) None of the above